To date, most of the sonar transmitters with a high power in low frequency, i.e. for frequencies ranging between 100 Hz and 10 kHz, generally comprise an engine, which is made of one or more stacks of electroacoustic plates, usually piezoelectric ceramics separated by electrodes.
Thus, the transducers known under the name of Tonpilz comprise a stack of similar plates, which are placed between a flare and a countermass and which are crossed by a stem which connects the flare to the countermass and which is energized to keep the plates pressed.
Transducers named "flextensional" are also known which comprise one or more stackings of similar electroacoustic plates laid out along the large axis of an envelope having an elliptic-shaped section.
Most of the time, the plates constituting a stacking are piezoelectric ceramics rings, with a plane lateral surface, which are separated by electrodes, so that the stacking has the shape of a straight cylinder with a circular section. In U.S. Pat. Nos. 2,988,728 and 3,495,102, the presented stackings have circular or annular plates which are chamfered for a better distribution of the stresses and to increase the distance between the electrodes in order to reduce the risk of breakdown.
Whatever is the geometrical shape of the plates, chamfered or not, the dimensioning of stacking is carried out mainly by determining the number and dimensions (thickness and diameter) of the plates for the considered frequency to be equal to the resonance frequency of the stacking.
However, for this type of dimensioning, the conditions required to obtain a low resonance frequency are in contradiction with those required to obtain a high power of emission, thus the realization of high power transducers is not possible.
Indeed, the resonance frequency F of a stacking is as follows ##EQU1## formula in which e represents the elasticity and m the mass of the stacking. The mass m being limited by limitations of weight and dimensions not to be exceeded, the coefficient on which it is possible to act is thus the elasticity e of the stacking. However, the elasticity: ##EQU2## formula in which Y is the Young's module, L the length and S the contact surface between the plates which is equal to the cross section of the plates.
The length L being also limited by limitations of dimensions not to be exceeded, the coefficient on which it is possible to act to reduce the resonance frequency by increasing elasticity is thus the section S which must be reduced.
The acoustic power Pa emitted by a stacking of piezoelectric ceramic plates is expressed by the following formula Pa=V.multidot.w.multidot.E.sup.2 .multidot.k.sup.2 .multidot..epsilon..multidot.Qm, formula in which V is the volume of the stacking, w the pulsation corresponding to the frequency, E the electric field applied to the stacking which is limited by the ceiling voltage, k the electromechanical coupling coefficient of the ceramics which depends on the kind of material, .epsilon. the dielectric constant of the ceramics and Qm a coefficient of quality which depends on the width of the passband and which is thus imposed by the choice of this width. This formula shows that the volume V of the stacking is one of the coefficients on which it is possible to act to increase the emitted power.
In the case of a straight cylindrical bar, the volume V is equal to the product of the length by the cross section.
As it has been already explained, the maximum length L is limited for reasons of dimensions.
If the cross section S is increased, the emitted power is increased, but as it has been explained previously, the elasticity of the stacking is reduced and thus the resonance frequency is increased, thus it is obvious that the choice of dimensions (thickness and diameter of the plates) as well as their number, is not sufficient to obtain at the same time a high power and a low frequency of emission.